While Supergirl fans may have guessed that Mon-El is Prince of Daxam for a while, Kara herself finally discovered the truth. After learned that her boyfriend both lied to her and was integral to an alien culture she despised, Kara broke up with Mon-El on Supergirl. However, while their relationship may be over, Mon-El isn't back to his old ways.
Freshly dumped, Mon-El ran right back to his parents, but didn't join them. The old him, the Prince, was someone he no longer recognizes and doesn't want to be. Girlfriend or not, Kara makes him a better Daxamite, and so he's sticking around. That also, hopefully, means that Teri Hatcher and Kevin Sorbo will stick around as his royal kin. Honestly, I wish that Kara was there to hear him correct his parents and call her a "woman" instead of a girl. His own personal growth was more important in that moment, but it was still pretty hot.
I do think that Kara was too quick to call it off with Mon-El, but I'm not surprised. This is kind of a pattern with her. Kara has trouble with trust, intimacy, and abandonment issues — serious problems that rarely ever to deal with because she's too busy being a superhero. I really like the way that Supergirl is handling her character. Too often, "strong female characters" have to be strong all the time. Even someone as chipper, positive, and extraverted as Kara Zor-El can struggle with anxiety and their mental well-being. It's one of my favorite, often subtle, things about this show.
While there's nothing wrong with being single, and Mon-El was certainly in the wrong, the fact that Kara's first reaction is to push people away isn't great either. That said, maybe Supergirl will use this opportunity to allow Kara a break from constant romantic drama. She needs it!
Kara also has a good point — Mon-El has family and a whole culture to return to. As someone who has truly lost those things, she would kill (well, not really kill) for that opportunity. This is a complicated turn of events, and I'm glad that Mon-El's story isn't over on Supergirl.